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### September 2017

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Author:
Rotem Liss
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Entanglement is an important concept in quantum information, quantum communication, and quantum computing. We provide a geometrical analysis of entanglement and separability for all the rank-2 quantum mixed states: complete analysis for the bipartite states and partial analysis for the multipartite states. For each rank-2 mixed state, we define its unique Bloch sphere, that is spanned by the eigenstates of its density matrix. We characterize those Bloch spheres into exactly five classes of entanglement and separability, give examples for each class, and prove that those are the only classes.

Joint work with Michel Boyer and Tal Mor.

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Author:
Tal Mor
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More than thirty years ago Feynman and Deutsch came up with the quantum computer. A decade later Peter Shor had shown the incredible power of quantum computers - for example, their ability to factorize large numbers, an ability whose technological consequences for the world of internet encryption and banking can be devastating.

In the last years the Wolf Prize, the Nobel Prize, and the Shannon’s Prize were given to researchers promoting quantum information and computing technologies, and the DWAVE startup has sold "quantum
simulators" to Lockheed Martin, as well as to Google and NASA. Is the future here? Or will we have to wait for it for a few more decades?

The answer depends upon whom you ask. In this presentation I will try to clearly present the current situation of this field.

Author:
Yoshiko Ogata
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We introduce a class of gapped Hamiltonians on quantum spin chains, which allows asymmetric edge ground states. We investigate the property, characterize it by physical conditions, and classify it.

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Author:
Karol Życskowski
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Properties of random mixed states of dimension $N$
distributed uniformly with respect to the Hilbert-Schmidt measure are
investigated. We show that for large $N$, due to the concentration of measure
phenomenon, the trace distance between two random states tends to a fixed  number
$1/4+1/\pi$, which yields the Helstrom bound on their distinguishability. To
arrive at this result we apply free random calculus and derive the symmetrized Marchenko--Pastur
distribution. Asymptotic value for the root fidelity between two random states,
$\sqrt{F}=3/4$, can serve as a universal reference value
for further theoretical and experimental studies.
Analogous results for quantum relative entropy and
Chernoff quantity provide other bounds on the distinguishablity of both states
in a multiple measurement setup due to the quantum Sanov theorem. Entanglement
of a generic mixed state of a bi--partite system is estimated.

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